An early goal from 20-year-old Dale Carrick and another in stoppage time from 19-year-old Billy King gave Hearts the points - a defeat would have confirmed their relegation - as Hibs were themselves sucked into deeper trouble at the wrong end of the table.
Alan Maybury was sent off near the end, which Butcher accepted, but the Hibs manager was upset that a Jordan Forster header was disallowed instead of standing as an equaliser. Assistant referee Alasdair Ross flagged for offside when in fact Forster was clearly played on by Dylan McGowan.
"It's made difficult by a horrendous decision," said Butcher. "The way things are going for us at the moment, it's pretty much par for the course. It's just so disappointing when it's a great header, a great goal and it wasn't even close to being offside.
"We had momentum at that stage, scoring in front of our fans, attacking our fans in the second half. We felt that if we got one goal we could get more, go on and win the game.
"I had a few words with the linesman as I went up the tunnel. I don't care to repeat them. There was no explanation given. It wasn't really close. Unbelievable. It was one of very few decent crosses, a great header, you're thinking it's 1-1 and great."
Hibs have now won only one of their last 12 SPFL Premiership games and are only six points above St Mirren in the relegation play-off place. "Am I worried? I'm concerned that we're not scoring goals," added Butcher. "And I'm concerned that we're shipping goals in. We need to get more points, simple as that.
"We've had a frank and open discussion. We need to pull our fingers out and get points on the board. We've got six games left, six games where we need to pick up as many points as possible.
"Teams gained ground on us over the weekend. It's only us who can ensure that we get as many points as we can. To do that, we've got to have guts and bravery on the edge of the box, make sure that we finish off the moves we've started."
Gary Locke, the Hearts manager, was delighted to prevent derby rivals Hibs getting the win which would have confirmed relegation. "It was a game we were very determined to win because we knew the outcome if Hibs had won," he said. "We're delighted to give the fans something to shout about, they've not had a lot to shout about. It's been a long hard season for us all and that result was for them.
"I had a sleepless night. I've had hundreds of sleepless nights. I'm sick of spending money on Nivea face cream to get rid of the wrinkles."
The Hibs support arrived in triumphant mood before being silenced. Goalscorer Carrick said: "We wanted to end their party and start ours."
When asked if Hibs might be relegated too, he said: "There is a possibility that could happen. Would I like to see that happen? Yeah, it's great having the derbies so we might as well have them next season."